How Do You Calculate Charge and Current Change Rate in LC Circuits?

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In LC circuits, the total energy can be calculated using the formula E = (1/2) C V^2, which helps determine the charge on the capacitor. For a circuit with a capacitance of 15 microfarads and total energy of 5.0*10^-6 J, the charge is found to be 12 microC. Additionally, in a circuit with an inductance of 15 mH and capacitance of 10 µF, if the charge on the capacitor is 25 µC, the current change rate is calculated to be 170 A/s. The discussion highlights the need for specific equations related to LC circuits, particularly the differential equations for series LC circuits, to solve these problems effectively. Understanding these concepts is crucial for analyzing charge and current changes in LC circuits.
dwn
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I'm having a difficult time finding any information in regards to LC circuits.

The total energy in an circuit is 5.0*10^-6 J. If C= 15 microfarads, what is the charge
on the capacitor? the ans is 12 microC

An circuit has an inductance of 15 mH and a capacitance of 10 µF. At one instant
the charge on the capacitor is 25 µC. At that instant the current is changing at what rate?

ans : 170 A/s

Again, I am unable to find the formula/information to solve these equations. Can someone please tell me what I am missing. I know the inductance equations (RLC) , but I don't see any in our book that contain just LC.

Thank you.
 
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dwn said:
I'm having a difficult time finding any information in regards to LC circuits.

The total energy in an circuit is 5.0*10^-6 J. If C= 15 microfarads, what is the charge
on the capacitor? the ans is 12 microC

What is the equation for the energy stored on a capacitor in terms of the capacitance and voltage?

dwn said:
An circuit has an inductance of 15 mH and a capacitance of 10 µF. At one instant
the charge on the capacitor is 25 µC. At that instant the current is changing at what rate?

ans : 170 A/s

Again, I am unable to find the formula/information to solve these equations. Can someone please tell me what I am missing. I know the inductance equations (RLC) , but I don't see any in our book that contain just LC.

Thank you.

Write the differential equations for a series LC circuit. Does that help you to get to the answer?
 
Thread 'Correct statement about size of wire to produce larger extension'

Thread 'Correct statement about size of wire to produce larger extension'

The answer is (B) but I don't really understand why. Based on formula of Young Modulus: $$x=\frac{FL}{AE}$$ The second wire made of the same material so it means they have same Young Modulus. Larger extension means larger value of ##x## so to get larger value of ##x## we can increase ##F## and ##L## and decrease ##A## I am not sure whether there is change in ##F## for first and second wire so I will just assume ##F## does not change. It leaves (B) and (C) as possible options so why is (C)...
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